We have no evidence about submitting sites to Google will help it being indexed faster. Google search engines will not sit and wait your submission to start indexing your site then showing in their search results. No, never. The spiders (you can call them “bots” or “crawlers”) of Google will follow the links from exist websites to crawl all related webs and pages and make a very huge database about the sites on the internet automatically and actively.
If your site is new, you may hear that you have to submit it to Google Search Console to get being indexed faster, but even that, the submission does not guarantee anything. The spiders will find your site and index it in due time, stop worry about the idea of needing to “tell” Google about your site. And one more thing, Google search results were actually cached and it will take time before Google algorithm refreshing the caches and start new indexes. So don’t be rushed.
Instead of trying to plug your new site into Google database, you should better focus on initial content and submit them to social networks instead. That’s will be a good starting steps for a brand new website.
If you still doubt about what I say, you can read a message from Matt Cutts (the former head of the web spam team at Google) to understand how Google search engines actually work:
When you do a Google search, you aren’t actually searching the web. You’re searching Google’s index of the web, or at least as of it as we can find. We do this with software called spiders. Spiders start by fetching a few web pages, then they follow the links on those pages and fetch the pages they point to; and follow all the links on those pages, and fetch the pages they link to, and so on, until we’ve indexed a pretty big chunk of the web; many billions of pages stored on thousands of machines
– Matt Cutts
Here is the video that he explained everything in detail: